I hope you went and got a 2nd opinion. I was in your situation but another doctor told me that "within normal range" is just a general range and doesn't mean that it is the range that is best for you. In 2003, my TSH was .40 and 2005 it was 3.69 and I was having all the same signs/symptoms as you. I got the same response in addition to being told to consider that I am peri-menopausal. After I got my 2nd opinion, my meds were adjusted and I feel back to normal. I hope you are better now!!
Thyroid is not the only thing that can cause you those symptoms. Your age is an important factor. Could you be perimenopausal? You should have your female hormones checked. As you get older your periods get heavier and you can develop anemia which causes fatigue. Your others symptoms could be explained by low estrogen levels. Sometimes you have to really push a doctor to do further test to really find out what is the cause of your problems.
My levels are T3 uptake is 36,T4 total is 8.8, T7 is 3.2, TSH is 0.59. My hair is thinning and limp,tired and feeling down,always have cold hands,just don't feel good. Could it be my thyroid or something else? I'm taking bioidential hormones but no progesterone,because I have no uterus. That level id 0.31.
I just went and had my thyroid checked, my levels were the same, and my doc said given that I has the symptoms of thyroid disease... Same as what you mentioned in your post... She started me yesterday on Levothyroxine, 25 mcg. I haven't taken it yet so I don't know if it will work, this morning will be my first dose, if I get up the guts to take it, I've read a lot of side effects so now I'm worried about that. But anyway... Don't know if this helps or not, but they told me my levels were on the "high" side, again 4.1, same as yours. I would suggest going to an endocrinologist if you feel your doc isn't taking your seriously... Some of them are like that, unfortunately. Best wishes to you.